Due 1/15: Prove the Corollary stated in class.

Due 1/23: Prove that the existence of inverse in the definition of the formal groups can be deduced from the other axioms.  Prove that the map defined in the class O_K \to End(F_f) is a homomorphism. Given two elements f and g in F_\varpi, apart from [1]_{g, f}, can you find some other isomorphisms between them?

Due 1/30: Prove that if a \in Z_p, m \in Z, then (a choose m) \in Z_p. Prove the proposition on Newton polygon. Use it to prove the characterization of the totally ramified extension.